No phone can "serf" the web while on a call. However, GSM cellular providers' phones can surf the web while on a call. Moreover, as I mentioned in a previous AT&T's marquis feature is one of the reasons why the GSM network is unreliable. You can look up the old thread for yourself if you'd like specifics. Also, don't take my word for it, Consumer Reports has rated VZW as having the best network for the last 4 or 5 years.
On the other hand, the only thing that AT&T has that is appealing is the iphone, which is a great device, but is rapidly losing ground to Android phones. However, if apple released the iphone to VZW I guarantee that AT&T would lose a lot of their customers (aka churn). AT&T customers main complaint is At&t's unrelaible networks.
